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Obtaining exact value by approximate computations

Science China Mathematics 2007年第9期50卷 1361-1368页

作者： Jing-zhong ZHANG Yong FENG Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer ApplicationsChinese Academy of SciencesChengdu 610041China

Numerical approximate computations can solve large and complex problems *** have the advantage of high *** they only give approximate results,whereas we need exact results in some *** is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.

关键词： numerical approximate computation symbolic-numerical computation continued fraction 33F10

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A complete discrimination system for polynomials

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Science China(Technological Sciences) 1996年第6期39卷 628-646页

作者：杨路侯晓荣曾振柄 Laboratory for Automated Reasoning & Programming Chengdu Institute of Computer ApplicationsChinese Academy of SciencesChengdu 610041China

Given a polynomial with symbolic/literal coefficients,a complete discrimination system is a set of explicit expressions in terms of the coefficients,which is sufficient for determining the numbers and multiplicities of the real and imaginary *** it is of great significance,such a criterion for root-classification has never been given for polynomials with degrees greater than *** lack of efficient tools in this aspect extremely prevents computer implementations for Tarski’s and other methods in automated theorem *** remedy this defect,a generic algorithm is proposed to produce a complete discrimination system for a polynomial with any *** result has extensive applications in various fields,and its efficiency was demonstrated by computer implementations.

关键词： discriminant sequence revised sign list root-classification complete discrimination system.

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Spectral properties and geometric interpretation of R-filters

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Applied Mathematics and Mechanics(English Edition) 2009年第1期30卷 109-120页

作者：冷拓 Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications Chinese Academy of SciencesChengdu 610041 P. R. China

By applying the Fourier analysis, we study the spectral properties of R- filters. Further, we prove that R-filters are a generalization of least squares polynomial adjustment, and we give the geometric interpretation ... 详细信息

关键词： R-filter HP-filter spectral properties Fourier analysis Hess-matrix operator theory

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OBTAINING EXACT INTERPOLATION MULTIVARIATE POLYNOMIAL BY APPROXIMATION

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Journal of Systems Science & Complexity 2011年第4期24卷 803-815页

作者： Yong FENG Xiaolin QIN Jingzhong ZHANG Xun YUAN Laboratory of Computer Reasoning and Trustworthy Computation University of Electronic b'cience and 'l~ech-nology of China Chengdu 611731 China. Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications ChineseAcademy of Sciences Chengdu 610041 China Graduate University of Chinese Academy of Sciences Beijing100049 China. Laborutory of Computer Reasoning and 7Yustworthy Computation University of Electronic Science and Tech-nology of China Chengdu 611731 China. Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications ChineseAcademy of Sciences Chengdu 610041 China.

In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exact interpolating methods are often proposed for the exact results and approximate interpolating methods for the ap- proximate ones. In this paper, the authors study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.

关键词： Continued fraction multivariate interpolation numerical approximate computation symbolic-numerical computation Vandermonde determinant.

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A trustworthiness-based access control model in grid system

A trustworthiness-based access control model in grid system

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2009 International Conference on Computational Intelligence and Software Engineering, CiSE 2009

作者： Jin, Taige Qin, Xiaolin Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications CAS Chengdu 610041 China

ISBN: (纸本)9781424445073

In existent researches of trustworthiness-based grid access control systems, an important question has not been resolved well: what types of historical behaviors should be chosen to measure trustworthiness. An access control model based on trustworthiness is designed in this paper. To measure trustworthiness of a certain user when he accesses to relevant resource, two types of historical behaviors in grid are chosen, concluding the user accessing to all resources in the target resource domain and all users in the user domain accessing to target resource, and the performance of these two types of historical behaviors decides trustworthiness of the user together. Consequently, trustworthiness of a user is divided into two parts: trustworthiness of the target resource domain to the user and trustworthiness of target resource to the user domain. Then a method to compute trustworthiness is introduced, and a model based on the methods above is designed in detail. It is concluded from experimental results that with the grid system becoming larger and more dynamic, the model in our study is more efficient. ©2009 IEEE.

关键词： Access control models

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Checking RSC criteria for extended dixon resultant by interpolation method

Checking RSC criteria for extended dixon resultant by interp...

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7th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2005

作者： Yong, Feng Yaohui, Li Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications Academia Sinica 610041 Chengdu China

ISBN: (纸本)0769524532

Dixon Resultant method can eliminate many variables simultaneously. It is often used to solve a system of polynomial equations. However, the Dixon matrix is often singular, and the Dixon Resultant vanishes identically yielding no information about solutions for many algebraic and geometry problems. So, Extended Dixon Method (KSY method) was proposed for the case when the Dixon matrix is singular, but satisfies RSC criteria. However, checking RSC criteria and extracting a maximum nonsingular submatrix of Dixon matrix are symbolic methods, which restrict Extended Dixon Method to be applied in more fields. In this paper, based on polynomial interpolation theory, an efficient numerical algorithm is developed to check RSC criteria and to extract a maximum nonsingular submatrix of singular Dixon matrix. Combining with interpolation methods for computing determinant, our method can solve larger scale problems. Furthermore, our method can be carried out parallel. © 2005 IEEE.

关键词： Natural sciences computing

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A class of mechanically decidable problems beyond Tarski's model

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Science China Mathematics 2007年第11期50卷 1611-1620页

作者： Lu YANG~(1,2) Yong FENG~(1+) Yong YAO~1 1 laboratory for automated reasoning and programming,chengdu institute of computer applications,Chinese Academy of Sciences,chengdu 610041,China 2 institute of Theoretical Computing,East China Normal University,Shanghai 200062,China Laboratory for Automated Reasoning Programming Chengdu Institute of Computer Applications Chinese Academy of Sciences Chengdu 610041 China Institute of Theoretical Computing East China Normal University Shanghai 200062 China

By means of dimension-decreasing method and cell-decomposition,a practical algorithm is proposed to decide the positivity of a certain class of symmetric polynomials,the numbers of whose elements are *** is a class of mechanically decidable problems beyond Tarski *** implement the algorithm,a program nprove written in maple is developed which can decide the positivity of these polynomials rapidly.

关键词： symmetric polynomial inequality cell-decomposition Tarski's sentence Tarski's model mechanically decidable problem

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Numerical method for real root isolation of semi-algebraic system and its applications

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Journal of Computational and Theoretical Nanoscience 2016年第1期13卷 803-811页

作者： Ji, Zhenyi Wu, Wenyuan Feng, Yong Li, Yi Qin, Xiao Lin Sichuan Agricultural University Chengdu611830 China Chongqing Key Laboratory of Automated Reasoning and Cognition Chongqing Institute of Green and Intelligent Technology Chinese Academy of Science Chongqing400714 China Laboratory of Automated Reasoning and Programming Chengdu Institute of Computer Applications Chinese Academy of Science Chengdu610041 China

In this paper, based on the homotopy continuation method and the interval Newton method, an efficient algorithm is introduced to isolate the real roots of semi-algebraic system. Tests on some random examples and a variety of problems including transcendental functions arising in many applications show that the new algorithm reduces the cost substantially compared with the traditional symbolic approaches. © 2016 American Scientific Publishers All rights reserved.

关键词： Numerical methods

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Block group preserving correction methods for differential algebraic equations with multiple constraints

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Journal of Computational and Theoretical Nanoscience 2016年第7期13卷 4042-4049页

作者： Lu, Jianguang Qin, Xiaolin Feng, Yong Tang, Juan Laboratory of Automated Reasoning and Programming Chengdu Institute of Computer Applications Chinese Academy of Science Chengdu610041 China Chongqing Key Laboratory of Automated Reasoning and Cognition Chongqing Institute of Green and Intelligent Technology Chinese Academy of Science Chongqing400714 China University of Chinese Academy of Science Beijing100049 China

In this paper, we combine the Euler scheme with the block group preserving methods to obtain the high accuracy block group preserving techniques. High index differential algebraic equations (DAEs) may have hidden algebraic constraints. To solve the high-index DAEs or DAEs with multiple constraints, we propose block group preserving correction scheme (BGPCS) via exponential mapping and block modified group preserving correction scheme (BMGPCS) by considering multiple constraints. We block the nonlinear dynamical system with m constraints into m subsystems. Each subsystem uses group preserving correction scheme (GPCS) and modified group preserving correction scheme (MGPCS). Moreover, we give two necessary conditions of the block methods. The schemes provide single-step explicit time integrators for systems of DAEs. Some numerical examples are examined, showing that the BMGPCS works very well and the merits of the computational efficiency and accuracy of the method can be confirmed. © 2016 American Scientific Publishers All rights reserved.

关键词： Nonlinear dynamical systems

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Mechanical decision for a class of integral inequalities

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Science China(Information Sciences) 2010年第9期53卷 1800-1815页

作者： YANG Lu1,3,YU WenSheng1,2* & YUAN RuYi2 1Shanghai Key laboratory of Trustworthy Computing,Software Engineering institute,East China Normal University,Shanghai 200062,China 2The Key laboratory of Complex Systems and Intelligence Science,institute of Automation,Chinese Academy of Sciences,Beijing 100190,China 3laboratory for automated reasoning and programming,chengdu institute of computer applications,Chinese Academy of Sciences,chengdu 610041,China 1. Shanghai Key Laboratory of Trustworthy Computing Software Engineering Institute East China Normal University Shanghai 200062 China3. Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications Chinese Academy of Sciences Chengdu 610041 China2. The Key Laboratory of Complex Systems and Intelligence Science Institute of Automation Chinese Academy of Sciences Beijing 100190 China

A class of integral inequalities is transformed into homogeneous symmetric polynomial inequalities beyond Tarski model,where the number of elements of the polynomial,say n,is also a variable and the coefficients are functions of *** is closely associated with some open problems formulated recently by Yang et *** Timofte's dimension-decreasing method for symmetric polynomial inequalities,combined with the inequality-proving package BOTTEMA and a program of implementing the method known as successive difference substitution,we provide a procedure for deciding the nonnegativity of the corresponding polynomial inequality such that the original integral inequality is mechanically decidable;otherwise,a counterexample will be *** effectiveness of the algorithm is illustrated by some more examples.

关键词： integral inequality symmetric polynomial inequality Timofte’s dimension-decreasing method successive difference substitution mechanical decision inequality-proving package BOTTEMA

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